The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  X  1  1  1  1  0  1  X  0  X  1  1  X  1  0  1 X^2
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  X  0 X^2+X  X X^2 X^2+X X^2+X X^2+X  X  0 X^2+X X^2  X  0 X^2+X  X X^2+X X^2  0 X^2+X X^2  X X^2 X^2
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+34x^31+87x^32+76x^33+120x^34+148x^35+202x^36+252x^37+230x^38+248x^39+184x^40+164x^41+150x^42+76x^43+14x^44+20x^45+2x^46+6x^47+22x^48+10x^50+2x^56

The gray image is a linear code over GF(2) with n=152, k=11 and d=62.
This code was found by Heurico 1.16 in 29.3 seconds.